What is the solution for 9y^{''}+6y^'+y=0 ?

The solution for 9y^{''}+6y^'+y=0 is y=c_{1}e^{-t/3}+c_{2}e^{-t/3}t

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9y^{''}+6y^'+y=0

9 y^{^{''}} + 6 y^{^{'}} + y = 0

y = c_{1} e^{- \frac{t}{3}} + c_{2} e^{- \frac{t}{3}} t

Solution steps

9 y^{''} (t) + 6 y^{'} (t) + y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{t}{3}} + c_{2} e^{- \frac{t}{3}} t

y = c_{1} e^{- \frac{t}{3}} + c_{2} e^{- \frac{t}{3}} t

(2 y - x^{2} y) y^{^{'}} = x (y + 2)^{2}

y = \frac{sin ( 2 x ) + 3 cos ( x )}{x + 1}

\int csch (x) d x

3 x + \frac{x ^{\frac{1}{3}}}{3}

F (X) = X - ln (1 + X)

What is the solution for 9y^{''}+6y^'+y=0 ?
The solution for 9y^{''}+6y^'+y=0 is y=c_{1}e^{-t/3}+c_{2}e^{-t/3}t